IndisputableMonolith.Physics.RS_PHY_Structural_007
Defines a nonnegative domain cost functional and a strictly positive canonical threshold used as the structural certificate for RS physics claim 007. Physicists tracking cost-bounded recognition domains would cite the certificate inhabitation. The module packages elementary nonnegativity and positivity facts over the imported J-cost and RS constants.
claimA domain cost $C$ is defined so that $C\ge 0$ pointwise, together with a canonical threshold $\theta>0$. The module supplies an inhabited certificate packing these two structural facts for RS physics claim 007.
background
Recognition Science measures mismatch by the J-cost $J(x)=(x+x^{-1})/2-1$ (equivalently $\cosh(\log x)-1$), imported here from the Cost module. Constants supplies the RS-native tick $\tau_0=1$. Structural physics claims in this layer ask whether a domain-level cost stays nonnegative and whether a fixed positive threshold can serve as a comparison scale.
This module introduces a domain cost functional and a canonical threshold, then records nonnegativity of the cost and positivity of the threshold. Those two properties are the only structural content required for the 007 certificate; no dynamical evolution or mass-ladder arithmetic appears here.
proof idea
Definition-plus-certificate module. Domain cost and the canonical threshold are introduced as defs; nonnegativity and positivity are short lemmas over the Cost and Constants imports. The certificate structure bundles those lemmas, and inhabitation is a one-line constructor application. No deep forcing-chain argument is run inside the file.
why it matters in Recognition Science
Places a reusable structural certificate (nonnegative domain cost, positive canonical threshold) into the Physics layer under the RS_PHY_Structural_007 label. Downstream used-by edges are empty in the current graph, so the module is a leaf certificate rather than an intermediate lemma. It sits downstream of Cost and Constants only, and does not yet touch T5 J-uniqueness, the eight-tick octave, or the mass ladder; it merely freezes the cost-threshold interface those later claims may assume.
scope and limits
- Does not derive the explicit form of the domain cost from the Recognition Composition Law.
- Does not prove uniqueness of the canonical threshold.
- Does not connect the threshold to phi, the eight-tick period, or D=3.
- Does not establish any mass, coupling, or dynamical bound beyond nonnegativity and positivity.
- Does not discharge any forcing-chain step T0-T8.